(Fluid Mechanics: Fundamentals and Applications 4th Edition, Yunus Cengel and John Cimbala, problem 2-88)
I am having some trouble with the order of operations. In the case of the below equation:
$4\frac{\sqrt{\frac{1}{4}}}{1-\sqrt{\frac{1}{4}}{}}=1$
I do not see how it is true, but in reference to the problem it results from, it just has to be. No matter what I try, I get $4 = 1$. The problem that this originates from is attached as an image. Can someone please let me know whether the problem is with the textbook or with my calculations. This is a simple problem, and yet it is driving me crazy, so I would greatly appreciate some help.
After careful consideration, I believe that the author made an algebraic error. The author went from
$$\frac{y}{h-y}=\sqrt{\frac{\mu_{\text{lower}}}{\mu_{\text{upper}}}}$$
to
$$y = \frac{\sqrt{\frac{\mu_{\text{lower}}}{\mu_{\text{upper}}}}}{1-\sqrt{\frac{\mu_{\text{lower}}}{\mu_{\text{upper}}}}}h$$
I believe that the denominator should be a plus not a negative. Following this logic the answer would be $y=4/3$.